US has been conducting back-channel talks with North Korea for months

— -- Despite the bombastic rhetoric exchanged between North Korean and American leaders this week, the Trump administration has been quietly engaged in back-channel diplomacy with North Korea for several months, according to a source familiar with the negotiations.

The ongoing talks, which were first reported by The Associated Press, included discussions about U.S.-North Korean relations and Americans imprisoned in North Korea, the source said.

The case of American student Otto Warmbier, who died following his release from North Korea, was included in those talks.

The U.S. State Department did not comment on the AP report.

Despite White House condemnations after Warmbier’s death, those contacts have continued and include discussions about the remaining Americans held there, the source said.

According to the source, the talks are being held between Ambassador Joseph Yun, the U.S. special representative for North Korea policy, and Pak Song Il, a senior North Korean diplomat at the country's U.N. mission, using what’s known as the “New York channel,” which has been an avenue of communication between the U.S. and North Korea throughout the years.

The talks ramped up after President Donald Trump’s inauguration, according to the source familiar with the negotiations, with the U.S. side aiming to secure the release of Warmbier and the other Americans held in North Korea.

A number of Trump administration officials, including the president himself, have publicly commented on the recent threats made by North Korea, including a proposed strike on the waters off Guam, a U.S. territory in the western Pacific.

Trump and Secretary of Defense James Mattis have both used strong language pertaining to North Korea's threats. But Mattis said Thursday that the American effort was "diplomatically led."

"What I would say here ladies and gentleman, my portfolio, my mission, my responsibility is to have military options should they be needed," he said.

"However, right now Secretary [of State Rex] Tillerson and [United Nations] Ambassador [Nikki] Haley, you can see the American effort is diplomatically led, it has diplomatic traction it is gaining diplomatic results, and I want to stay right here, right now. The tragedy of war is well known. It would be catastrophic."

Earlier this week, Trump said that North Korea would be met with "fire and fury" if it made further threats against the U.S., and then on Thursday, he suggested that those words may not have been "tough enough" after the threats from North Korea continued.